Voronoi and Delauney

Via socialfiction :i really like these mathematical constructions that can be generated by this applet. Especially the Voronoi diagram, also called the Thiessen diagram : a set of polygons, each one containing exactly one of the given points, and all other points in the plane which are closer to that point than to any of the other given points. It is also known as the Thiessen diagram or the Dirichlet Tessellation.

The voronoi reminds me vegetals cells !!!! :
CONNECTION TO MY RESEARCH here : http://www.snibbe.com/scott/bf/. According to them : "The regions [personal space] which surrounds each person are mathematically referred to as Voronoi diagrams or Dirichlet tessellations"

The Delauney is good as well : This option draws the Delauney Triangulation of the points. If you draw the Convex Hull (see below) of the points, there are many ways to divide the convex hull into triangles, that is, to triangulate it. The Delauney triangulation is the triangulation with the smallest total edge length. It is related to the Voronoi diagram by duality, that is, the vertices, edges and faces of the one correspond exactly to the faces, edges and vertices (in that order) of the other :